Bernhard Beckermann, Emmanuel Bourreau
How to choose modified moments?
Key words : Orthogonal polynomials, Modified moments, Modified Chebyshev algorithm.
Classifications: AMS(MOS): 65D20, 33C45.

Abstract

Modified moments of a non-negative measure determine uniquely the recurrence coefficients of the polynomials orthogonal with respect to the given non-negative measure. The sensitivity of the underlying non-linear maps with regard to perturbations in the modified moments has been studied by Gautschi, and is further analyzed in this paper. In particular we discuss the question of how (not) to choose the support of the underlying two measures.